PHYSICAL REVIEW B 94, 104512 (2016)

Superconducting properties of noncentrosymmetric Nb0.18Re0.82 thin films probed bytransport and tunneling experiments

C. Cirillo,1,2 G. Carapella,1,2 M. Salvato,1,3 R. Arpaia,4 M. Caputo,1,2 and C. Attanasio1,2

1CNR-SPIN Salerno, Universita degli Studi di Salerno, I-84084 Fisciano (SA), Italy2Dipartimento di Fisica “E.R. Caianiello”, Universita degli Studi di Salerno, I-84084 Fisciano (SA), Italy

3Dipartimento di Fisica Universita di Roma “Tor Vergata”, I-00133 Roma, Italy4Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience,

Chalmers University of Technology, SE-41296 Goteborg, Sweden(Received 17 June 2016; revised manuscript received 3 August 2016; published 16 September 2016)

Superconducting thin films of the noncentrosymmetric superconductor Nb0.18Re0.82 were successfullydeposited by UHV sputtering technique. X-ray diffraction analysis indicated that the films are polycrystalline,with a preferential (nn0) orientation and the lattice parameter in agreement with the expected single α-Mn cubicphase. A detailed electrical characterization of the samples as a function of the thickness (3.5 nm � d � 142 nm)was performed both in the normal and in the superconducting states, revealing a well-established superconductingordering, as well as an estimated value of the upper critical field, μ0Hc2, comparable with the Pauli limit.Finally, the symmetry of the order parameter was probed by tunneling spectroscopy on Al/Al2O3/Nb0.18Re0.82

heterostructures, which provides evidence for a single s-wave superconducting gap.

DOI: 10.1103/PhysRevB.94.104512

I. INTRODUCTION

Recently, superconducting materials lacking in the inver-sion symmetry in their crystal structure were intensivelyinvestigated due to the possible exotic nature of their su-perconducting order parameter, which in the presence of astrong antisymmetric spin-orbit scattering, could in principlebe a mixture of spin-singlet and spin-triplet components[1]. Moreover, under appropriate conditions, topologicallynontrivial superconducting states can also be realized inthese systems [2]. Experimental verification of both thesepossibilities is of extreme fundamental and applicative interest[3]. In addition, in the normal state antisymmetric spin-orbitscattering may be responsible for intriguing transport phenom-ena connecting charge and spin currents [1,4], on which theemergent field of spin orbitronics is based [5,6]. The presenceof an unconventional superconducting pairing seems to bewell established for some heavy fermion noncentrosymmetricsuperconductors (NCS) such as CePt3Si [7] or CeRhSi3 [8,9].At the same time, superconductors with heavy transitionelements may be more straightforward systems for exploringthe consequences of inversion symmetry breaking. Indeed, insome cases exotic pairing was detected, as for instance inLi2Pt3B [10,11], whereas for some other compounds, such asRe6Zr [12,13] or BiPd [14–17], the results are still controver-sial. In particular, BiPd is especially interesting since for thismaterial topologically nontrivial surface states were reportedin the normal state [16]. Among transition-metal compounds,NbxRe1−x is a NCS which can be a possible candidate forhaving a nonconventional superconducting order parameter.Since Re is a heavy element, the effect of the antisymmetricspin-orbit scattering, the main ingredient affecting the pairingsymmetry in these materials, is expected to be strong inthe regime of low Nb percentage. The results observedon polycrystalline bulk samples were controversial [18–20],while the recent investigation [21] performed by combiningpoint contact spectroscopy and heat capacity measurementson high quality Nb0.18Re0.82 single crystals [22] evidenced

the presence of two superconducting gaps. However, furtherexperimental investigations are needed, since the employedmeasurement techniques did not provide enough insight to thesymmetries of these two order parameters. Moreover, all theexperimental studies on NCS focused so far on bulk samples,apart from preliminary attempts to produce Li2Pt3B films[23], even if the possibility to produce NCS in the form ofthin films is of extreme importance. First, the availability ofNCS thin films may allow one to design dedicated transportexperiments on heterostructures which are more sensitive tothe spin symmetry of the superconducting order parameter[24,25]. Second, should the unique electronic properties ofthese materials be confirmed, any NCS-based device wouldemploy them in a thin film form.

In this work noncentrosymmetric NbxRe1−x thin films weredeposited and characterized and tunneling experiments wereperformed in order to determine the pairing symmetry of thesuperconducting order parameter in this system. The paper isorganized as follows. Section II is devoted to the experimentalresults, namely, the samples fabrication (Sec. II A), the x-rayanalysis (Sec. II B), and the electrical characterization both inthe normal (Sec. II C) and in the superconducting (Sec. II D)state. In Sec. II E the conductance spectra measured onAl/Al2O3/NbRe junctions as a function of the temperatureare presented and analyzed. Finally, in Sec. III the issue of thetriplet component of the superconducting order parameter isdiscussed and in Sec. IV the conclusions are reported.

II. EXPERIMENT

A. Sample fabrication

NbxRe1−x films of different thickness (d = 3.5–200 nm)were grown on Si(100) substrates by UHV dc diode magnetronsputtering from a Nb0.20Re0.80 99.9% pure target. The deposi-tion was performed keeping the substrate at room temperaturein an Ar pressure of 3 × 10−3 mbar after obtaining a basepressure in the low 10−8 mbar regime. The deposition rate

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was 0.32 nm/s, as measured by a quartz crystal monitorpreviously calibrated by low-angle x-ray reflectivity (XRR)measurements on a deliberated deposited thin film. The Nbconcentration, as estimated by energy diffraction spectroscopy(EDS), was x = 0.18. Therefore the resulting Nb0.18Re0.82

(hereafter NbRe) films are close to the optimal Nb concentra-tion in terms of superconducting transition temperature, Tc, asreported in the case of bulk samples [19]. The Al/Al2O3/NbRejunctions were realized as follows. A 60-nm-thick, 100-μm-wide Al strip was deposited on a Si/SiO2 substrate by rfmagnetron sputtering and patterned by photolithography andlift-off. The Al deposition was performed keeping the substrateat room temperature in an Ar pressure of 3.2 × 10−3 mbar froma base pressure in the low 10−7 mbar regime. The depositionrate was 1.2 nm/s resulting in a roughness lower than 1 nm, asmeasured by atomic force microscopy. The insulating barrierwas obtained by thermal oxidation of the Al strip in airat room temperature for several hours. In these conditionsthe thickness of grown Al2O3 is estimated to be saturated[26] at ∼1.5 nm. Then a 100-nm-thick, 100-μm-wide NbRecounter electrode was deposited by dc sputtering as describedpreviously, and patterned by photolithography and lift-off tocross the bottom Al/Al2O3 strip. The resulting junction areais A = (100 × 100) μm2 with cross geometry that allows oneto perform four contact measurements. With this method theresistance per area product of the junctions was in the rangeof R · A ∼ M�μm2. Such a large figure suggests that one ispossibly concerned with reliable, pinhole-free tunnel barriers.

B. X-ray characterization

Low-angle reflectivity measurements, performed with ahigh resolution x-ray diffractometer with CuKα radiation,on a typical NbRe film of nominal thickness of 20 nm, arereported in Fig. 1 by open circles. The red line is the numericalsimulation of the measured XRR profile, as obtained by usingthe software package GIXA using d = 19 nm and surfaceroughness of σ = 1.0 nm.

FIG. 1. Experimental (open circles) and simulated (red line) XRRprofile for a NbRe thin film 19-nm thick.

NbRe (330)

Si (004)NbRe (330)

FIG. 2. XRD 2θ -ω scan of a NbRe film 200-nm thick. The insetshows the ω scan (rocking curve) of the (330) Nb0.18Re0.82 reflection.

The structural properties of the films were accuratelydetermined by x-ray diffraction (XRD), performed with a four-circle Panalytical X’pert diffractometer with CuKα radiation,using a hybrid Ge(220) monochromator and a PIXcel 3Ddetector matrix.

The crystalline structure of the films was determined bysymmetric 2θ -ω scans, as shown in Fig. 2 for a NbRe filmwith d = 200 nm. First of all, it should be noticed that no peakscorresponding to the single phases of Nb and Re are detected.Indeed, the primary peak, at 2θ ≈ 40◦, can be consistentlyindexed as the (330) reflection, corresponding to the mostintense peak expected for the noncentrosymmetric α-Mn cubicphase of NbRe [19,20]. From the peak position, a latticeparameter a = 0.957 nm is estimated, a value which is in goodagreement with the expected one for the Nb0.18Re0.82 structure[18–20,27]. The large shape of this reflection indicates a smallmean crystallite size within the film [28]. Moreover, the filmis polycrystalline, as confirmed by the flat rocking curvemeasured on the (330) reflection (see inset of Fig. 2) [29].This occurrence is an indication of a disordered structure, asalso the large broadening of the primary peak in 2θ suggests.In this respect, efforts to optimize the quality of the NbRefilms, by establishing a better matching between the films andthe substrates, as well as by tuning the sputtering conditions(e.g., deposition temperature and rate) will be the object offuture studies.

C. Normal state transport properties

Dealing with the first deposited NbRe films it is mandatoryto perform a detailed electrical characterization of the samplesalso in the normal state. This analysis could in principlebe useful also for future studies focusing on the nontrivialcoupling between charge and spin degrees of freedom in thenormal state. All the transport measurements were performedeither in a liquid helium Dewar or in a 4He cryostat, withthe substrates glued with silver paint to a massive coppersample holder. The dc transport properties presented in thissection were performed on unpatterned samples. A van derPauw four leads configuration [30] was used to determine the

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FIG. 3. Thickness dependence of the ratio β10. Inset: electricalresistivities ρ300 (red circles) and ρ10 (black squares) as a function ofthe NbRe thickness. The dashed line indicates the value of the lowtemperature resistivity reported for Nb0.18Re0.82 single crystals [22].

samples resistivity, ρ. A constant current, Ib = 0.5 mA, wasapplied to bias the samples. In the main panel of Fig. 3 thethickness dependence of the residual resistivity ratio, definedas the ratio between the value of the resistance at T = 300 Kand T = 10 K (β10 = R300/R10), is reported. Here β10, whichquantifies the overall degree of purity and crystal perfection ofa film, monotonically increases with the film thickness. Thisbehavior, commonly reported for films of finite thickness, canbe ascribed to the increase of the average grain size with d [31].Its value stays below unity for the entire investigated thicknessrange, and tends to saturate to β10 ≈ 1 for the thicker films.This result is typical of disordered superconductors, such asNbN [32,33]. It is worth reminding the reader that also in thecase of NbRe single crystals [21] and polycrystalline samples[18] the values of β10 were relatively low, namely, β10 ≈ 1.14and 1.35, respectively. The comparison with the bulk valuemay suggest that the β10 values are not affected by structuralissues. The thickness dependence of the resistivities, evaluatedboth at T = 300 K and T = 10 K (ρ300 and ρ10, respectively),are reported in the inset of Fig. 3. Unexpectedly, both theresistivities increase with increasing the film thickness and itis also worth noticing that their saturation value is close tothe one reported for NbRe single crystals [22] (dashed line).It is well known that conventional metallic superconductorsusually present an opposite ρ(d) dependence, which can beascribed either to finite size effects [34], or to grain boundaryscattering [31]. In particular, for both single Nb [35,36] andRe [37] thin films ρ decreases with increasing thickness.This point, together with the issue of the value of β10 willbe investigated in the following, when also the values of thesuperconducting critical temperatures will be shown. Finally,following Ref. [38] the measured values of ρ10, together withthe value of the electron-phonon (e-ph) coupling constant [18],λe-ph = 0.73, seem to indicate that all the films are in theweak-coupling regime. This point will be further analyzed inthe section devoted to tunneling experiments.

5.0 5.5 6.0 6.5 7.0 7.5 8.00.0

0.2

0.4

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10

T (K)

d (nm)142954719107.05.03.5

0 20 40 60 80 100 120 1405.0

5.5

6.0

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Tc (K

)Tc

(K)

d (nm)

(b)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

FIG. 4. (a) Normalized resistive transitions for some of the mea-sured NbRe films. (b) Thickness dependence of the superconductingcritical temperature Tc (left scale) and the amplitude of the resistivetransitions, Tc (right scale). The solid line is the fit to the Tc(d) dataaccording to the model in Ref. [39].

D. Superconducting properties

1. NbRe thin films

Following the deposition procedure described in Sec. II A,NbRe films with well established superconducting orderingwere realized. As for the crystallographic properties, also thesuperconducting ones confirm that no spurious phases arepresent in the samples. The normalized resistive transitions,R/R10, of a selection of unpatterned NbRe films are reportedin Fig. 4(a). The superconducting critical temperature wasdefined as the temperature at which the resistance is half ofthe one measured at T = 10 K, Tc ≡ T 50%

c . For the thickestmeasured film (d = 142 nm) Tc = 7.40 K, a value which isabout one Kelvin lower than the one reported for single crystalswith the same composition [21]. As can be better inferred frompanel (b) of Fig. 4 (left scale), Tc is a monotonically increasingfunction of the film thickness, as for Nb [35,36] and Re [37],with a stronger dependence for d � 20 nm. The oppositedependence is found for the width of the resistive transitions,defined as Tc = T 90%

c − T 10%c [Fig. 4(b), right scale]. In

fact, the transitions become sharper as d increases. Both ofthese last two dependencies indicate that the superconductingproperties are strengthened as the film thickness is increased,

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FIG. 5. Dependence of the critical temperature, Tc, on β10 (a)and ρ (b).

as commonly reported for conventional superconductors. Inparticular, it is interesting to point out that the thinnest film(d = 3.5 nm) still presents a noticeable critical temperature of5.3 K. The decrease of Tc as a function of the film thicknessis typically ascribed to the presence of the external surfaceof the film. This effect was studied in Ref. [39], where thefollowing dependence was derived: Tc = T b

c (1 − dcr/d). HereT b

c is the critical temperature of the bulk superconductor anddcr = 2b/N (0)V is the critical thickness below which Tc = 0[here b is the Thomas-Fermi screening length and N (0)V is thebulk interaction potential]. The result of the fitting procedureon the Tc(d) data using this last expression is reported inFig. 4(b) as a solid line. Very good agreement is obtainedwith the parameters T b

c = 7.43 K and dcr = 1.0 nm. Theextremely reduced value of the critical thickness is consistentwith the small values of the superconducting coherence length,ξ (0) = 4.3 nm, reported for NbRe polycrystals [18] [theevaluation of ξ (0) for the samples investigated here will bepresented in the following]. It is well known, in fact, thatthe reduction of Tc with the thickness is more effective ford ≈ ξ . In Fig. 5(a) the dependence of the critical temperatureon β10 is shown. This behavior resembles that reported forNb films [40], while it is opposite to the result obtained forRe films [37]. This point will be discussed below in termsof the position of the Fermi level in the density of statesof these two materials. Finally, in Fig. 5(b) the dependenceof the transition temperature on ρ is reported. Contrary tothe results reported for both Nb [35,40] and Re [37], hereTc increases with increasing resistivity. Again, this behaviorwas reported in the literature for a variety of disordered films[41], such as irradiated Mo3Ge [42]. In this last work thedisorder induced by the radiation resulted in an enhancementof Tc, of the residual resistivity, and according to the authors,also of the value of the density of states in Mo3Ge withoutreducing the electron-phonon interaction. Summarizing, theresults reported in Fig. 5, as well as in the previous section,

FIG. 6. Selection of resistive transition as a function of thetemperature for different values of the magnetic field for a NbRepatterned film 60-nm thick. Inset: dependence of electrical resistanceon the magnetic field, R(μ0H ), at T = 4.25 K, in the low field region.

suggest that the transport properties are dominated by disorder.Tc increases or decreases with disorder depending on theshape of the density of states at the Fermi level N (0). Forweak-coupling superconductors, with low values of N (0), andconsequently low values of bulk Tc, such as Re, disorderdetermines an increase in N (0). The opposite occurs for Nb,which has a peak at N (0). In this case the smearing inducedby disorder on the density of states, can produce a drop in Tc

[42,43]. This observation further suggests that NbRe is in theweak-coupling regime.

2. NbRe bridges

In the following the electric transport measurements per-formed in the presence of a magnetic field are reported. For thispurpose, the samples were structured into a Hall bar geometryof width w = 100 μm and distance between the voltagecontacts L = 1 mm. In order to determine the value of theupper critical magnetic field at T = 0, μ0Hc2(0), resistance-vs-temperature, R(T ), measurements were performed at fixedvalues of the magnetic field close to Tc, with Ib = 10 μA.A selection of the R(T ) curves measured on a NbRe Hallbar with d = 60 nm is reported in the main panel ofFig. 6 for μ0H = 0, 0.09, and 0.18 T. As in the case ofbulk polycrystals, the width of the transitions increases byincreasing the magnetic field [18]. By adopting the sameresistance criterion reported above and extrapolating the lineardependence of μ0Hc2(T ) down to T = 0, it follows thatμ0Hc2(0) = 14.4 ± 0.9 T. With the assumption of a lineardependence of the perpendicular upper critical field, it is alsopossible to evaluate the superconducting coherence length,since μ0Hc2(0) = �0/2πξ (0)2, where �0 = 2.07 × 10−15

Wb is the flux quantum [44]. This relation gives ξ (0) = 4.8 nm.From the value of Tc = 7.3 K and that of the low temperatureresistivity ρ10 = 148 μ� cm it is possible to extract the valueof the magnetic penetration depth at zero temperature fromthe relation [45] λ(0) = 1.05 × 10−3(ρ10/Tc)0.5 = 472 nm.

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Therefore the Ginzburg-Landau parameter is κ = λ/ξ = 98.The knowledge of these microscopic parameters allows one toestimate the value of the lower critical field [44] μ0Hc1(0) =(�0/4πλ2)ln(λ/ξ ) = 3.4 × 10−3 T and of thermodynamiccritical field [44] μ0Hc(0) = κ

√2μ0Hc1(0)/lnκ = 0.10 T, in

reasonable agreement with the results on bulk polycrystals[18]. Moreover, from the slope of the μ0Hc2(T ) curve thevalue of the quasiparticle diffusion coefficient D can beestimated [46], since D = (4kB/πe)(μ0dHc2/dT |T =Tc

)−1 =0.56 × 10−4 m2/s, with (μ0dHc2/dT |T =Tc

) = −2.0 T/K. Fi-nally, in the inset of Fig. 6 the low field region of the mag-netoresistance curve [R(μ0H )] measured on the same sampleis shown. The curve, acquired at T = 4.25 K, with a biascurrent of Ib = 10 mA, was used for a further estimation of thevalue of μ0Hc2(0), as will be described in the following. V (I )characteristics were also measured on the same samples withd = 60 nm. Electrical interference was minimized, filtering allcables with RC filters. Very low noise V (I ) characteristics aswell as differential conductance-voltage curves, G(V ), wererecorded using the 6221 current source/2182A nanovoltmetercombo from Keithley. In the upper inset of Fig. 7(a) a selectionof the V (I ) characteristics at T = 4.25 K (corresponding to areduced temperature t = T/Tc = 0.58) are shown. The curveswere measured for different values of the magnetic field, fromzero up to μ0H = 0.88 T, which was applied perpendicularlyto the sample surface. The main panel of Fig. 7(a) shows thedependence of the critical current density Jc = Ic/(wd) on themagnetic field in a reduced field range (see discussion below).The critical current Ic was defined using a voltage criterionVc = 1 μV, which corresponds to an electric field criterionEc = 1 nV/m. At zero magnetic field Jc(0) = 8.3 × 109 A/m2,a value which is comparable to the ones reported for Nb thinfilms [47]. From the analysis of the Jc(μ0H ) dependence,information concerning the pinning strength of NbRe can begained [48,49]. As shown in the lower inset of Fig. 7(a) bythe dot-dashed line, in the low field regime, the critical currentdensity decreases linearly with μ0H , until Jc is reduced tohalf its value at zero field. This behavior is usually observed,together with a μ0H

−1 dependence at higher fields, whenthe main pinning source is the bridge’s edge [48]. Here aweaker field dependence is observed at higher fields, as can beinferred from the main panel of Fig. 7(a). The dashed line,which corresponds to the μ0H

−1 dependence, lays belowthe experimental data in the entire investigated field range,while the solid one, which represents the μ0H

−1/2 dependence,nicely reproduces the measured points up to μ0H = 0.05 T, asreported for materials with stronger pinning, such as TaN [49].An even weaker decrease is present for μ0H � 0.05 T (for thesake of clearness, here the data were shown up to μ0H = 0.2T), which indicates that edge pinning is absent in the NbRefilm in this field range. From the analysis of the V (I ) curvesin the low voltage region, as shown in the inset of Fig. 7(b),it emerges that a linear voltage-current behavior, typical of aflux-flow regime, is always present even at very low currentbias. It is worth commenting also on the sudden transitionwhich follows the linear regime. Indeed, a clear jump to thenormal state occurs at a current I ∗, corresponding to a voltageV ∗ [see inset of Fig. 7(b)]. This point will be analyzed later.Now, since in the flux-flow regime [44] Rf /Rn = H/Hc2(0),where Rf (Rn) is the flow (normal) resistance, from the linear

FIG. 7. (a) Dependence of the critical current density on themagnetic field, Jc(μ0H ), for the same sample of Fig. 6 at T = 4.25 K.The dashed line shows the μ0H

−1 field dependence, as expected whenthe dominant pinning mechanism is due to the bridge edge. By thecontinuous line the μ0H

−1/2 behavior is reported. The upper insetshows some representative V (I ) curves for different values of themagnetic field, from zero up to μ0H = 0.88 T. In the lower panelthe low field regime of the Jc(μ0H ) curve is reported, in order tohighlight the linear field dependence (dot-dashed line), also due toedge pinning. (b) Dependence of the critical velocity, v∗, as a functionof the magnetic field, μ0H , at T = 4.25 K. Inset: V (I ) curves shownon a small voltage range at T = 4.25 K for increasing magnetic field(as indicated by the arrow) from μ0H = 0.01 T to μ0H

max = 0.88 T.The definition of both the current I ∗ and the voltage V ∗ are indicatedfor the sake of clearness.

fit of the V (I ) curves it is possible to estimate the value ofthe upper critical magnetic field at T = 0 and to compare itwith the one extracted from the R(T ) curves. It results thatμ0H

V (I )c2 = 14.4 ± 0.3 T. Finally, the same analyses were also

performed on the R(μ0H ) curve reported in the inset of Fig. 6.From a linear fit of the low field region, according to thesame expression valid in the flux-flow regime, it results that

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TABLE I. Values of the parameters which characterize the 60-nm-thick NbRe patterned film, as extracted from the V (I ), R(H ),and R(T ) curves.

Parameters Estimated values

Tc (7.3 ± 0.1) Kρ10 148 μ� cmμ0Hc1(0) 3.4 × 10−3 Tμ0Hc2(0) (14.4 ± 0.9) Tμ0(dHc2/dT )T =Tc

(−2.0 ± 0.1) T/Kμ0Hc(0) 0.10 Tξ (0) 4.8 nmλ(0) 472 nm

μ0HRHc2 (0) = 15.0 ± 0.3 T. It follows that all the estimations

of μ0Hc2(0) are in agreement within the experimental error.Returning to the issue of the jump in the V (I ) curves

[see inset of Fig. 7(b)], it is well known that the voltage V ∗corresponding to the value of the current I ∗, where the jumpsare detected, can be interpreted as the Larkin and Ovchinnikovflux-flow instability at the velocity v∗. Following Ref. [50], itis V ∗ = μ0v

∗HL and the critical velocity can be expressed asv∗ = D1/2[14ζ (3)]1/4(1 − t)1/4/πτ

1/2E , which means that from

measuring the critical voltage V ∗ it is possible to estimate thevalues of the quasiparticle relaxation times, τE . Here ζ (x) isthe Riemann zeta function and D is the quasiparticle diffusioncoefficient. In Fig. 7(b) the dependence of the critical velocityon the magnetic field at T = 4.25 K is reported. At very lowfields a peak is present, as already observed for differentsuperconducting materials both in the nonmesoscopic [51],as well as in the mesoscopic regime [52]. From the valuesof v∗, it follows that the values of the relaxation time att = 0.58 span from τmin

E = 2.3 × 10−11 s at μ0H = 0.003 T(corresponding to the peak in the field dependence of v∗), toτmaxE = 1.3 × 10−9 s at μ0H = 0.88 T. By comparing these

values with those reported in the literature [53], it seems thatin NbRe the energy relaxation processes are faster than inNb and of the same order of magnitude as in NbN, which,due to the extremely reduced characteristic e-ph couplingtime [54], is characterized by the extremely reduced valueof τE . This result could also be ascribed to the disorder presentin the sample, since it can cause an appreciable reductionof the quasiparticles lifetimes [53,55]. In Table I all theparameters estimated for the 60-nm-thick patterned sample aresummarized.

E. Tunneling spectroscopy

Useful information on the order parameter of a supercon-ductor can be extracted by analysis of differential conductancecurves, G(V ), of tunnel junctions [44,56] or point contactswithin the model of Blonder, Tinkham, and Klapwijk (BTK)[57] and its extensions [58]. Here the tunnel junction method,which is more suited for thin films, was chosen. In thefabricated N-I-S tunnel junctions, the superconductor (S) isNbRe, the normal metal (N) is Al, and the thin insulator (I) isAl2O3, the reliable native oxide of Al. A sketch of the junction,which illustrates the four contact measurement configuration,

FIG. 8. Normalized conductance spectra (points) of a tunneljunction are fitted with the BTK model (lines). The geometry ofthe measured tunnel junction is shown in the left inset. The energygap (T ) and the broadening parameter �(T ) as estimated from thefit are shown in the right inset. The estimated (T ) (points) can benicely fitted with the BCS behavior (line).

is shown in the left inset of Fig. 8. From the analysis of severaljunctions similar results were obtained. For the representativejunction reported here, the normal state resistance at T =7.5 K was RN ≈ 398 � (RA ≈ 4 M�μm2) and the criticaltemperature of the NbRe counterelectrode was Tc ≈ 7.20 K. Arepresentative set of the G(V ) curve of this junction at severaltemperatures is shown in the main panel of Fig. 8. In orderto allow a direct comparison with theory, the conductancecurves are normalized to the conductance in the normal stateat 7.5 K, GN = 1/RN . At first glance, the conductance spectrasuggest that a standard BCS [44,59] order parameter is possiblyexhibited by the polycrystalline NbRe films. In fact, theexperimental spectra can be satisfactorily fitted with the BTKmodel [57], which assumes a single isotropic order parameterwith s-wave symmetry. Some representative fitting curves areplotted in the main panel of Fig. 8. Even though a reasonablefit was achieved also within the simple version of the model, amore satisfactory agreement was achieved applying the BTKmodel [58,60], which includes the broadening parameter �

introduced by Dynes et al. [61]. As usual [58,60], in the fits atemperature-independent barrier strength [57] parameter Z, atemperature-dependent superconducting gap amplitude (T ),and a temperature-dependent broadening parameter �(T ) wereassumed. The best fits were achieved with Z = 3, a resultwhich confirms that a tunnel regime is realized. In agreementwith the finding of Dynes et al. [61], the broadening parameteris found to be reasonably small at the lowest temperature[�(4.25 K) = 0.02 meV] and to increase with temperature.This value is consistent with the estimate of the relaxationtime evaluated in the previous section. Indeed, τE = �/�,therefore at T = 4.25 K and H = 0 it is τE = 3.3 × 10−11 s,in reasonable agreement with the value resulting from the V (I )analysis for τmin

E . The values of (T ) and �(T ) extracted fromthe fits of all the measured conductance curves are shown inthe right inset of Fig. 8. The (T ) is found to be well fitted with

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the BCS behavior [44,59] using (0) and T (fit)c as parameters.

The best fit is achieved with (0) = 1.08 ± 0.02 meV andT (fit)

c = 7.20 ± 0.01 K, i.e., the critical temperature of theused NbRe counterelectrode, a value which is in agreementwith the Tc of a plane NbRe film of the same thickness[see Fig. 4(b)]. A comparison of the estimated value of theenergy gap at zero (0) with the one expected from BCSrelation [44] BCS(0) = 1.76kBTc ≈ 1.09 meV confirms thatthe NbRe films under investigation are weak-coupling [44]superconductors.

III. DISCUSSION

Having performed a deep characterization of the NbRefilms deposited, it is worth comparing the obtained resultswith those reported in literature for bulk samples, bothin polycrystalline [18–20] and in single crystal [21] form.Concerning the microscopical parameters extracted from thetransport measurements, apart from the values of the criticaltemperature at the saturation as a function of the thickness,which is depressed of about 1 K with respect to the bulkvalue, there is general agreement between the values of thephysical parameters extracted for the films and the bulk.The low temperature resistivity of the thickest film ρ10 =133 μ� cm is slightly lower than the one reported for singlecrystals [22] and for polycrystals of Ref. [19], but higherthan the one estimated on other polycrystalline samples ofRef. [18]. The low residual resistivity ratio found here iscompatible with the values of β10 of single- [21] and poly-[18] crystals, namely, β10 = 1.14 and β10 = 1.35, respectively.The values of the coherence length ξ (0) = 4.8 nm are in goodagreement with the figures reported in previous works forbulk NbRe [18,19]. On the contrary, as expected for a film,the penetration depth λ(0) = 472 nm is larger compared tothe bulk. A general accordance holds for the values of thecritical fields. Particularly interesting is, in this respect, thehigh values estimated for the perpendicular upper critical fieldat zero temperature (between 14 and 15 T), since this result isgenerally interpreted as a possible fingerprint of the presence ofa triplet component of the order parameter. Indeed, as found forsome polycrystalline samples [18,19], here μ0Hc2(0) is closeto the Pauli limiting field, which can be obtained from thetunneling measurements as μ0HPauli = (0)/(μB

√2) = 13

T. The temperature-dependent tunneling spectra on the firstjunctions based on NbRe films are fully compatible with aBCS single gap order parameter. A different result was recentlyobtained performing soft point contact spectroscopy on NbResingle crystals [21], where a two-gap structure described by atwo-band model with isotropic spin-singlet pairing symmetrywas observed. This controversial result may possibly originatefrom the lack of directionality in the tunnel experiment.Indeed, for both point contact and tunnel experiments, it ishighly desirable to perform direction-controlled spectroscopy

in order to control the direction of the current injection withrespect to the crystallographic axes [62]. Unfortunately, thiscondition was not fulfilled here, since, as revealed by the XRDdata, the films are not epitaxial. Indeed, an unconventionalpairing, if present, could be hindered by an averaging over thedifferent crystallographic orientation. Moreover, as reportedin Ref. [63], the presence of defects or impurities couldaffect the unconventional pairing. Therefore, as for the bulksamples the debated results obtained on polycrystals [18–20]stimulated the investigation of single crystals; similarly here,the investigation of epitaxial films would cast a new lighton the nature of the pairing symmetry in NbRe. Indeed, finetuning of the deposition conditions is in progress in order toenhance the film quality and, consequently, to perform morereliable direction-controlled experiments to access the wavesymmetry of the superconducting order parameter, using bothsingle films as well as heterostructures [24,25].

IV. CONCLUSIONS

In conclusion, superconducting Nb0.18Re0.82 films with thedesired crystallographic ordering were successfully depositedon Si(100) substrates. The samples were deeply characterized,both structurally and electrically. XRD measurements showthat the films are polycrystalline, with a preferred (nn0) growthwhich is compatible with the noncentrosymmetric α-Mnstructure expected for this composition [27]. The transportproperties seem to be strongly influenced by disorder; nev-ertheless, the films exhibit well established superconductingproperties. Attention was devoted to the investigation of thenature of the superconducting order parameter. In this respectthe values of μ0Hc2(0) comparable to μ0HPauli could inprinciple support the possible presence of an unconventionalpairing [18,19]. On the other hand, tunnel conductance spectra,measured on high quality Al/Al2O3/NbRe tunnel junctionsrealized on NCS materials, can be described by a single gaps-wave model, providing strong evidence for conventionalsuperconducting pairing. Finally, from the estimated valueof the superconducting order parameter at T = 0, it followsthat the ratio (0) = 1.76kBTc indicates a weak electron-phonon coupling. Deeper insight is expected from tunnelingexperiments on epitaxial films. Moreover, the successfulrealization of reliable NbRe-based hybrid systems opens thepossibility for further studies devoted to both unveiling theissue of the nature of the superconducting order parameter andtaking advantage of the antisymmetric spin-orbit scattering inthe normal state.

ACKNOWLEDGMENTS

The authors gratefully acknowledge Dr. R. Fittipaldi for theEDS analysis, Professor J. Aarts for the XRR measurements,and Dr. M. Cuoco for useful discussions.

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